Sarah needs to purchase organic palm oil to make her soaps. She needs 1,000 kg of palm oil per day on average. The supplier charges a $60 delivery fee per order (which is independent of the order size) and $4.75 per kg. Sarah's annual holding cost is 25%. Assume 52 weeks per year and 5 days per week. If Sarah wants to minimize inventory holding and ordering costs, how much palm oil should she purchase with each order (in kg)? (Round your answer to the nearest whole number.)

Practical Management Science
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Sarah's Organic Soap Company makes four kinds of organic liquid soap: regular, lavender, citrus, and tea tree.
The demand for the four scents are 150, 120, 75, and 50 kg per hour respectively. Sarah's production process
can produce any soap at the rate of 450 kg per hour, but 1.5 hours are needed to switch between scents. During
those switchover times, the process doesn't produce any soap. Sarah wants to choose a production schedule
that (i) cycles repeatedly through the four scents, (ii) meets the required demand and (iii) minimizes the amount
of inventory held.
Sarah needs to purchase organic palm oil to make her soaps. She needs 1,000 kg of palm oil per
day on average. The supplier charges a $60 delivery fee per order (which is independent of the
order size) and $4.75 per kg. Sarah's annual holding cost is 25%. Assume 52 weeks per year and 5
days per week. If Sarah wants to minimize inventory holding and ordering costs, how much palm oil
should she purchase with each order (in kg)? (Round your answer to the nearest whole
number.)
5,126 kg
5,226
5,326
5.426
Transcribed Image Text:Sarah's Organic Soap Company makes four kinds of organic liquid soap: regular, lavender, citrus, and tea tree. The demand for the four scents are 150, 120, 75, and 50 kg per hour respectively. Sarah's production process can produce any soap at the rate of 450 kg per hour, but 1.5 hours are needed to switch between scents. During those switchover times, the process doesn't produce any soap. Sarah wants to choose a production schedule that (i) cycles repeatedly through the four scents, (ii) meets the required demand and (iii) minimizes the amount of inventory held. Sarah needs to purchase organic palm oil to make her soaps. She needs 1,000 kg of palm oil per day on average. The supplier charges a $60 delivery fee per order (which is independent of the order size) and $4.75 per kg. Sarah's annual holding cost is 25%. Assume 52 weeks per year and 5 days per week. If Sarah wants to minimize inventory holding and ordering costs, how much palm oil should she purchase with each order (in kg)? (Round your answer to the nearest whole number.) 5,126 kg 5,226 5,326 5.426
Expert Solution
Step 1

Annual demand = 52 weeks X 7 days a week X 1000kg per day = 364000 kg

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